Grow your
brain
Yellow
Guaranteed to
make your brain
grow, just add
some effort and
hard work
5
The wee
Maths Book
of
Big
Brain
Growth
Volume and Nets
Don’t be afraid if
you don’t know
how to do it, yet!
It’s not how fast
you finish, but that
you finish.
It’s always better
to try something
than to try nothing.
Don’t be worried
about getting it
wrong, getting it
wrong is just part
of the process
known better as
learning.
Volumes
M15s
(MTH 2-11c, MTH 3-11a, MTH 3-11b)
I can find the volumes of solids such as cubes, cuboids
and other solids by counting cubes.
In each of the questions below, there are two views of the same pile of
cubic centimetres. Find the volume of each pile of cubes.
1.
2.
3.
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4.
5.
6.
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7.
Each of the cuboids below are made from piling up cubic centimetres
Find the volume of each cube.
(a)
(b)
(c)
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M16s
1.
I can comfortably convert between litres, millilitres
and cubic centimetres.
Write the volume of each of the following items in litres.
(a)
(b)
(c)
2000 cm3
1400 cm3
350 cm3
(d)
(e)
(f)
5 ml
568 cm3
150 ml
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(g)
(h)
(i)
500 ml
750 ml
3500 cm3
(j)
(k)
(l)
5000 cm3
330 ml
160000 cm3
2.
3.
Write the volume of each of the following items in millilitres.
(a) 160 litres
(b) 50 litres
(c) 2 litres
(d) 0·333 litres
(e) 4 litres
(f) 0·5 litres
(g) 0·568 litres
(h) 0·75 litres
(i)
0·05 litres
For each of your answers in Q2, give an example, from real life, of a
container which would normally contain that volume.
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M17t
1.
I can calculate the volume of a variety of 3D shapes
including prisms by applying a formula
A fish tank is 55 cm long, 40 cm wide and 25 cm high, as shown.
25 cm
40 cm
55cm
(a) What formula would you use to calculate the volume of the tank?
(b) Calculate how much water you need to fill the tank to the top.
(c) Another fish tank holds twice the amount of water.
How much water do you need to fill it to the top?
2.
Calculate the volume of each of the following shapes:
(a)
(b)
3cm
cube
5cm
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6cm
4cm
3.
The volume of this cuboid is 3600cmᵌ.
Calculate the height of the cuboid.
h
c
m
12cm
15cm
4.
Find the volume of the prisms shown.
(a)
(b)
(c)
(d)
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5.
A fish tank is 40 cm long, 25 cm wide and 20 cm high, as shown.
20 cm
25 cm
40cm
(a) What formula would you use to calculate the volume of the tank?
(b) Calculate how much water you need to fill the tank to the top.
6.
Calculate the volume of each of the following shapes:
(a)
(b)
4cm
cube
8cm
7.
5cm
10cm
The volume of this cuboid is 3600cmᵌ.
Calculate the height of the cuboid.
h
c
m
12cm
15cm
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8.
Find the volume of the prisms shown.
(a)
(b)
Area
Area
= 12cm2
= 5m2
10m
6cm
(c)
(d)
Area
Area
= 100cm2
= 40m2
13m
25cm
(e)
(f)
Area
= 64m2
Area
= 43cm2
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0·5m
150cm
9.
The diagram shows a triangular prism.
The dimensions are given on the diagram.
(a) Calculate the area of the cross section of the prism.
(b) Calculate the volume of the prism.
10.
The diagram shows another triangular prism.
The dimensions are given on the diagram.
2m
5m
3m
(a) Calculate the area of the cross section of the prism.
(b) Calculate the volume of the prism.
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M18t
1.
Having investigated different routes to a solution, I can
find volume of compound 3D objects (cuboids only),
applying my knowledge to solve practical problems.
The diagram shows two compound shapes made from cuboids.
The dimensions are given on the diagrams.
Find the volume of each shape.
(a)
(b)
2.
The volume of the
prism, shown below,
can be calculated using
the prism formula or
from the fact that it is
made up from
compound cuboids.
Find the volume using the two
methods and check that in both cases
the answers are equal.
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3.
Again, the volume of the prism, shown below, can be calculated
using the prism formula or from the fact that it is made up from
compound cuboids.
Again, find the volume
using the two methods and
check that in both cases
the answers are equal.
4.
Calculate the volume of the shape shown below.
Is the shape a prism?
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3D Shape (MTH 2-16a, MTH 2-16b, MTH 2-16c)
S16s
1.
I can use appropriate mathematical language when
referring to 3D shapes using words such as faces, edges
and vertices
Below is a diagram of a triangular prism.
(a) How many faces does it have?
(b) How many vertices does it have?
(c) How many edges does it have?
2.
Below is a diagram of a square based pyramid.
(a) How many faces does it have?
(b) How many vertices does it have?
(c) How many edges does it have?
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S17s
I can recognise and name three-dimensional shapes
from their two-dimensional representations: cube,
pyramid, cylinder, cuboid, cone and sphere
1.
Pick the correct net
for the cone.
2.
Pick the correct net for the
triangular prism.
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3.
Pick the correct net for the
hexagonal prism.
4.
Pick the correct net for the cylinder.
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5.
Pick the correct net for the
square based pyramid.
6.
Pick the correct net for the cube
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S18s
I can construct a 3D shape from their net of (cube,
cuboid and triangular Prism).
1.
Complete the “Net of a Cube worksheet”.
2.
Complete the “Net of a Cuboid worksheet”.
3.
Complete the “Net of a Triangular Prism worksheet”.
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S19s
I can make a 2D drawing to represent a cube or a
cuboid.
1.
On squared paper draw three different nets of a cube.
2.
Which of the following nets below represent a net of a cube
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
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A well nurtured and emotionally healthy pupil will know that
they can improve their brain power through regularly applying
themselves to his/her studies in class and by completing all of
the tasks in this booklet.
He/she will feel more included, respected and will develop greater levels of
responsibility if you regularly discuss with them their progress, both progress
in class and progress through this booklet.
You will encourage him/her to be a passive learner and intellectually lazy if
you show them how to attempt every question. Encourage them to think for
themselves. Your child will achieve more if they actively experiment with
the questions in this booklet, safe in the knowledge that they can learn from
any mistakes made.
Tips for Parents
1.
Talk to your child on a regular basis about the work they are
attempting in Mathematics.
2.
Give praise for appropriate effort and resilience, and avoid praise
which uses the words clever or smart.
3.
Talk about your child's brain power improving through hard work
and not being something that is fixed.
4.
Mistakes are part of the learning process. Your child should be able
to experiment with Maths safe in the knowledge that they can learn
from their mistakes.
5.
Talk about your child’s progress in a way which emphasises their
own ability to influence a positive and successful future. This will
encourage them to become more resilient and equipped to meet
the challenges of the course.
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